Equal Friction

Part 2. Air Distribution | Chapter 2. Air Duct Design

CHART 7 – FRECTION LOSS FOR ROUND DUCT


TABLE 6 – CIRCULAR EQUIVALENT DIAMETER,*EQUIVALENT AREA AND DUCT CLASS†OF RECTANGULAR DUCTS FOR EQUAL FRICTION.


TABLE 6 – CIRCULAR EQUIVALENT DIAMETER,*EQUIVALENT AREA AND DUCT CLASS†OF RECTANGULAR DUCT FOR EQUAL FRICTION. (Cont.)


TABLE 6 – CIRCULAR EQUIVALENT DIAMETER,*EQUIVALENT AREA AND DUCT CLASS†OF RECTANGULAR DUCTS FOR EQUAL FRICTION. (Cont.)


TABLE 7 – RECOMMENDED MAXIMUM DUCT VELOCITIES FOR LOW VELOCITY SYSTEMS (FPM)

TABLE 8 – VELOCITY PRESSURES

NOTES: 1. Data for standard air (29.92 in Hg and 70 F) 2. Data derived from the following equation:

hv = ( )2V4005

Where: V = velocity in fpm. hv = pressure difference termed”velocity head” (in. wg).


FAN CONVERSION LOSS OR GAINIn addition to the calculations shown for determining

the required static pressure at the fan discharge inExample 4, a fan conversion loss or gain must beincluded. This conversion quantity can be a significantamount, particularly on a high velocity system. It isdetermined by the following equations.

If the velocity in the duct is higher than the fan outletvelocity, use the following formula for the additional staticpressure required:

Loss = 1.1

where Vd = duct velocityVf = fan outlet velocity

Loss = in. wgIf the fan discharge velocity is higher than the duct

velocity, use the following formula for the credit taken tothe static pressure required:

Gain = .75

DUCT SYSTEM ELEMENT FRICTION LOSSFriction loss thru any fitting is expressed in terms of

equivalent length of duct. This method provides units thatcan be used with the friction chart to determine the loss ina section of duct containing elbows and fittings. Table 12gives the friction losses for rectangular elbows, and Table11 gives the losses for standard round elbows. Thefriction losses in Table 11 and 12 are given in terms ofadditional equivalent length of straight duct. This loss forthe elbow is added to the straight run of duct to obtain thetotal equivalent length of duct. The straight run of duct ismeasured to the intersection of the center line of the

fitting. Fig. 46 gives the guides for measuring ductlengths.

Rectangular elbows may be classified as either hardor easy bends. Hard bends are those in which the depth(depth measured in the radial direction) of the elbow isgreater than the width. Hard bends result in significantlyhigher friction losses than do easy bends and thereforeshould be avoided. See note for Table 12, p. 2-44.

Table 9 and 10 list the friction losses fir other sizeelbows or other R/D ratios. Table 10 presents the frictionlosses of rectangular elbows and elbow combinations interms of L/D. Table 10 also includes the losses andregains for various duct shapes, stream of the duct. Thisloss or regain is expressed in the number of velocityheads and is represented by “n”. This loss or regain maybe converted into equivalent length of duct by theequation at the end of the table and added or subtractedfrom the actual duct length.

Table 9 gives the loss of round elbows in terms ofL/D, the additional equivalent length to the diameter of theelbow. The loss for round tees and crosses are in terms ofthe number of velocity heads (“n”). The equation forconverting the loss in velocity head to additionalequivalent length of duct is located at the bottom of thetable.

In high velocity systems it is often desirable to havethe pressure drop in round elbows, tees, and crosses ininches of water. These losses may be obtained fromChart 9 for standard round fittings.DESIGN METHODS

The general procedure for designing any ductsystem is to keep the layout as simple as possible andmake the duct runs symmetrical. Supply terminals andlocated to provide proper room air distribution (Chapter3), and ducts are laid out to connect these outlets. Theductwork should be located to avoid structural membersand equipment.

The design of a low velocity supply air system maybe accomplished by any one of the three followingmethods:

1. Velocity reduction2. Equal friction3. Static regainThe three methods result in different levels of

accuracy, economy and use.The equal friction method is recommended for return

and exhaust air systems.LOW VELOCITY DUCT SYSTEMSVelocity Reduction Method

The procedure for designing the duct system by thismethod is to select a staring velocity at the fan discharge

2 2)[( Vd4000 ( )Vf

4000 ]-

2 2)[( Vf4000 ( )Vd

4000 ]-

CHART 8 – PRESSURE DROP THRUFLEXIBLE CONDUIT



TABLE 10 – FRICTION OF RECTANGULAR DUCT SYSTEM ELEMENTS


TABLE 10 – FRICTION OF RECTANGULAR DUCT SYSTEM ELEMENTS (Contd)


NOTES FOR TABLE 9*L and D are in feet. D is the elbow diameter. L is the additional equivalent lengthof duct added to the measured length. The equivalent length L equals D in feettimes the ratio listed.†The value of n is the loss in velocity heads and may be converted to additionalequivalent length of duct by the following equation.

Where : L = additional equivalent length, ft hv = velocity pressure at V2, in. wg (conversion line on

Chart 7 or Table 8). hf = friction loss/100 ft, duct diameter at V2, in. wg

(Chart 7). n = value for tee or cross‡ Tee or cross may be either reduced or the same size in the straight thruportion

NOTES FOR TABLE 10*1.25 is standard for an unvaned full radius elbow.†L and D are in feet. D is the duct diameter illustrated in the drawing. L is theadditional equivalent length of duct added to the measured duct. The equivalentlength L equals D in feet times the ratio listed.‡The value n is the number of velocity heads or differences in velocity headslost or gained at a fitting, and may be converted to additional equivalent length ofduct by the following equation.

Where : L = additional equivalent length, ft hv = velocity pressure for V1, V2 or the differences in. velocity pressure,

in wg (conversion line on Chart 7 orTable 8).

hf = friction loss/100 ft, duct cross selection at hv, in. wg(Chart 7).

n = value for particular fitting.

L = n x hv x 100hf

L = n x hv x 100hf

TABLE 11 – FRICTION OF ROUND ELBOWS


TABLE 12 – FRICTION OF RECTANGULAR ELBOWS


TABLE 12 – FRICTION OF RECTANGULAR ELBOWS (CONT.)


CHART 9 – LOSSES FOR ROUND FITTINGSElbows, Tees and Crosses


and make arbitrary reductions in velocity down the ductrun. The starting velocity selected should not exceedthose in Table 7. Equivalent round diameters may beobtained from Chart 7 using air velocity and air quantity.Table 6 is used with the equivalent round diameter toselect the rectangular duct sizes. The fan static pressurerequired for the supply is determined by calculation,using the longest run of duct including all elbows andfittings. Table 10 and 12 are used to obtain the lossesthru the rectangular elbows and fittings. The longest runis not necessarily the run with the greatest friction loss, asshorter runs may have more elbows, fitting andrestrictions.

This method is not normally used, as it requires abroad background of duct design experience andknowledge to be within reasonable accuracy. It should beused only for the most simple layouts. Splitter dampersshould be included for balancing purposes.Equal Friction Method

This method of sizing is used for supply, exhaust andreturn air duct systems and employs the same friction lollper foot of length for the entire system. The equal frictionmethod is superior to velocity reduction since it requiresless balancing for symmetrical layouts. If a design has a

mixture of short and long runs, the shortest run requiresconsiderable dampering. Such a system is difficult tobalance since the equal friction method makes noprovision for equalizing pressure drops in branches of forproviding the same static pressure behind each airterminal.

The usual procedure is to select an initial velocity inthe main duct near the fan. This velocity should beselected from Table 7 with sound level being the limitingfactor. Chart 7 is used with this initial velocity and airquantity to determine the friction rate. This same frictionloss is then maintained throughout the system and theequivalent round duct diameter is selected from Chart 7.

To expedite equal friction calculations, Table 13 isoften used instead of the friction chart; this results in thesame duct sizes.

The duct areas determined from Table 13 or theequivalent round diameters from Chart 7 are used toselect the rectangular duct sizes from Table 6. Thisprocedure of sizing duct automatically reduces the airvelocity in the direction of flow.

To determine the total friction loss in the duct systemthat the fan must overcome, it is necessary to calculatethe loss in the duct run having the highest resistance. Thefriction loss thru all elbows and fittings in the section mustbe included.

TABLE 13 – PERCENT SECTION AREA IN BRANCHES FOR MAINTAINING EQUAL FRICTION


Example 4 – Equal Friction Method of Designing DuctsGiven:

Duct systems for general office (Fig.47).Total air quantity – 5400 cfm18 air terminals – 300 cfm eachOperating pressure forall terminals – 0.15 in. wgRadius elbows, R/D = 1.25

Find:1. Initial duct velocity, area, size and friction rate in the duct

section from the fan to the first branch.2. Size of remaining duct runs.3. Total equivalent length of duct run with highest

resistance.4. Total static pressure required at fan discharge.

Solution:1. From Table 7 select an initial velocity of 1700 fpm.

Duct area =

From Table 6, select a duct size-22 in.x22 in.Initial friction rate is determined from Chart 7 using the airquantity (5400), and the equivalent round duct diameterfrom Table 6. Equivalent round duct diameter = 24.1 in.Friction rate = .145 in. wg per 100 ft of equivalent length.

2. The duct areas are calculated using Table 13 and ductsizes are determined from Table 6. The followingtabulates the design information:

DUCTSECTION

AIRQUANTITY

(cfm)

CFM*CAPACITY

(%)To A 5400 100

A – B 3600 67B – 13 1800 3313 – 14 1500 2814 – 15 1200 2215 – 16 900 1716 – 17 600 1117 – 18 300 6

DUCTSECTION

DUCTAREA(%)

AREA†(sq ft)

DUCTSIZE‡

(in.)To A 100.0 3.18 22 x 22A – B 73.5 2.43 22 x 16B – 13 41.0 1.3 22 x 1013 – 14 35.5 1.12 18 x 1014 – 15 29.5 .94 14 x 1015 – 16 24.0 .76 12 x 1016 – 17 17.5 .56 8 x 1017 – 18 10.5 .33 8 x 10

† Duct area = percent of area times initial duct area (fan to A)

‡ Refer to page 21 for reducing duct size.

Duct sections B thru 12 and A thru 6 have the samedimension as the corresponding duct sections in B thru18.

3. It appears that the duct run from the fan to terminal 18has the highest resistance. Tables 10 and 12 are used todetermine the losses thru the fittings. The following list isa tabulation of the total equivalent length in this duct run:

DUCTSECTION ITEM LENGTH

(ft)

ADD.EQUIV.

LENGTH(ft)

To A Duct Elbow

6012

A – B Duct 20B – 13

--Duct Elbow

307

13 – 14 Duct 2014 – 15 Duct 2015 – 16 Duct 2016 – 17 Duct 2017 – 18 Duct 20

Total 210 19

4. The total friction loss in the ductwork from the fan to lastterminal 18 is shown in the following:

Total static pressure required at fan discharge is the sum of theterminal operating pressure and the loss in the ductwork. Creditcan be taken for the velocity regain between the first and lastsections of duct:

1700 fpm5400 cfm 3.18 sqft=

Loss = total equiv length X friction rate

*Percent of cfm = air quantity in duct sectiontotal air quantity

= 229 ft .145 in. wg100 ft = .332 or .33 in. wg

Fig. 47 – Duct Layout for Low Velocity System(Examples 4 and 5)


Velocity in initial section = 1700 fpmVelocity in last section = 590 fpmUsing a 75% regain coefficient,

Regain = .75

= .75(.18-.02) = .12 in. wgTherefore, the total static pressure at fan discharge: = duct friction + terminal pressure - regain = .33 + .15 - .12 = .36 in. wg

The equal friction method does not satisfy the designcriteria of uniform static pressure at all branches and airterminals. To obtain the proper air quantity at thebeginning of each branch, it is necessary to include asplitter damper to regulate the flow to the branch. It mayalso be necessary to have a control device (vanes,volume damper, or adjustable terminal volume control) toregulate the flow at each terminal for proper airdistribution.

In Example 4, if the fan selected has a dischargevelocity of 2000 fpm, the net credit to the total staticpressure required is determined as described under “FanConversion Loss or Gain:”

Gain = .75

= .75 (.25 - .18) = .05 in. wg

Static Regain MethodThe basic principle of the static regain method is to

size a duct run so that the increase in static pressure(regain due to reduction in velocity) at each branch or airterminal just offsets the friction loss in the succeedingsection of duct. The static pressure is then the samebefore each terminal and at each branch.

The following procedure is used to design a ductsystem by this method: select a starting velocity at the fandischarge from Table 7 and size the initial duct sectionfrom Table 6.

The remaining sections of duct are sized from Chart10 (L!Q Ratio) and Chart 11 (Low Velocity Static Regain).Chart 10 is used to determine the L/Q ratio knowing theair quantity (Q) and length (L) between outlets orbranches in the duct section to be sized by static regain.This length (L) is the equivalent length between theoutlets or branches, including elbows, excepttransformations. The effect of the transformation section isaccounted for in “Chart 11 3 Static Regain.” Thisassumes that the transformation section is laid outaccording to the recommendation presented in thischapter.

Chart 11 is used to determine the velocity in the ductsection that is being sized. The values of the L/Q ratio(Chart 10) and the velocity (V1) in the duct sectionimmediately before the one being sized are used in chart11. The velocity (V2) determined from Chart 11 is usedwith the air quantity to arrive at the duct area. This ductarea is used in Table 6 to size the rectangular duct and toobtain the equivalent round duct size. By using this ductsize, the friction loss thru the length of duct equals the increase in static pressure due to the velocity change aftereach branch take-off and outlet. However, there areinstances when the reduction in area is too small towarrant a change in duct size after the outlet, or possiblywhen the duct area is reduced more than is called for.This gives a gain or loss for the particular duct sectionthat the fan must handle. Normally, this loss or gain issmall and, in most instances, can be neglected.

Instead of designing a duct system for zero gain orloss, it is possible to design for a constant loss or gainthru all or part of the system. Designing for a constantloss increases operating cost and balancing time andmay increase the fan motor size. Although not normallyrecommended, sizing for a constant loss reduces theduct size.Example 5 – Static Regain Method of Designing DuctsGiven :

Duct layout (Example 4 and Fig. 47)Total air quantity – 5400 cfmVelocity in initial duct section – 1700 fpm (Example 4)Unvaned radius elbow, R/D = 1.2518 air terminals – 300 cfm eachOperating pressure for all terminals – 0.15 in. wg

Find :1. Duct sizes.2. Total static pressure required at fan discharge.

Solution :1. Using an initial velocity of 1700 fpm and knowing the air

quantity (5400 cfm), the initial duct area after the fandischarge equals 3.18 sq ft. From Table 6, a duct size of22” X 22” is selected. The equivalent round duct sizefrom Tale 6 is 24.1 in. and the friction rate from Chart 7 is0.145 in. wg per 100 ft of equivalent length. Theequivalent length of duct from the fan discharge to thefirst branch :

= duct length + additional length due to fitings= 60 + 12 = 72 ft

The friction loss in the duct section up to the first branch:= equiv length of duct X friction rate

= 72 X

The remaining duct sections are now sized.

(40001700[( ) ) ]590

400022-

40002000[( ) ) ]1700

400022- (


CHART 10 – L/Q RATIO

CHART 11 – LOW VELOCITY STATIC REGAIN


The longest duct run (A to outlet 18, Fig. 47) should besized first. In this example, it is desirable to have thestatic pressure in the duct immediately before outlets 1and 7 equal to the static pressure before outlet 13.Figure 48 tabulates the duct sizes.

2. The total pressure required at the fan discharge is equalto the sum of the friction loss in the initial duct sectionplus the terminal operating pressure.Fan discharge pressure:

= friction loss + terminal pressure= .104 + .15 = .25 in. wg

It is good design practice to include splitter dampersto regulate the flow to the branches, even though thestatic pressure at each terminal is nearly equal.Comparison of Static Regain and Equal Friction Methods

Example 4 and 5 show that the header duct sizedetermined by the equal friction or static regain methodare the same. However, the branch ducts, sized by staticregain, are larger than the branch ducts sized by equalfriction.

Figure 49 shows a comparison of duct sizes andweight established by the two methods.

The weight of sheet metal required for the systemdesigned by static regain is approximately 13% morethan the system designed by equal friction. However, thisincrease in first cost is offset by reduced balancing timeand operating cost.

If it is assumed that a low velocity air handling systemis used in Examples 3 and 4 and that a design air flow of5400 cfm requires a static pressure of 1.5 in. wg, Theincreased horsepower required for other equal frictiondesign is determined in the following manner.

STATICREGAIN

METHOD S.P.(in. wg)

EQUALFRICTION

METHOD S.P.(in. wg)

Air handling equipment 1.5 1.5Duct friction .104 .33Terminal pressure .15 .15Static regain credit - -.12Total 1.75 1.86

Additional hp = = 6.3%approx.

A 6% increase in horsepower often indicates a largerfan motor and subsequent increased electricaltransmission costs.

HIGH VELOCITY DUCT SYSTEMS

A high velocity air distribution system uses higher airvelocities and static pressures than a conventionalsystem. The design of a high velocity system involves acompromise between reduced duct sizes and higher fanhorsepower. The reduced duct size is a savings inbuilding space normally allotted to the air conditioningducts.

Usually Class II fans are required for the increasedstatic pressure in a high velocity system and extra caremust be taken in duct layout and construction. Ducts arenormally sealed to prevent leakage of air which maycause objectionable noise. Round ducts are preferred torectangular because of greater rigidity. Spira-Pipeshould be used whenever possible, since it is made oflighter gage metal than corresponding round andrectangular ducts, and does not require bracing.

Symmetry is a very important consideration whendesigning a duct system. Maintaining as symmetrical asystem as possible reduces balancing time, design timeand layout. Using the maximum amount of symmetricalduct runs also reduces construction and installationcosts.

Particular care must be given to the selection andlocation of fittings to avoid excessive pressure drops andpossible noise problem. Figure 50 illustrates the minimumdistance of six duct diameters between elbows and 90°tees. If a 90 ° conical tee is used, the next fitting in thedirection of air flow may be located a minimum of one-halfduct diameter away (Fig. 51). The use of a conical tee islimited to header ductwork and then only for increasedinitial velocities in the riser.

When laying out the header ductwork for a highvelocity system, there are certain factors that must beconsidered:

1. The design friction losses from the fan dischargeto a point immediately upstream of the first risertake-off from each branch header should be asnearly equal as possible. These points of thesame friction loss are shown in Fig. 52.

2. To satisfy the above principle when applied tomultiple headers leaving the fan, and to takemaximum advantage of allowable high velocity,adhear to the following basic rule whereverpossible: Make as nearly equal as possible theratio of the total equivalent length of each header

1.86 – 1.751.75


Fig. 48 – Duct Sizing Calculation Form

Fig. 49 – Comparison of Duct Sizing Methods


run (fan discharge to the first riser take-off) to theinitial header diameter (L/D ratio). Thus thelongest Spira-Pipe header run should preferablyhave the highest air quantity so that the highestvelocities can be used throughout.

3. Unless space conditions dictate otherwise, thetake-off from the header should be made using a90° tee or 90° conical tee rather than a 45° tee.By using 90° fittings, the pressure drop to thebranch throughout the system is more uniform. Inaddition, two fittings are normally required whena 45° tee is used and only one when a 90°fitting is used, resulting in lower first cost.

The design of a high velocity system is basically thesame as a low velocity duct system designed for staticregain. The air velocity is reduced at each take-off to theriser and air terminals. This reduction in velocity results ina recovery of static pressure (velocity regain) whichoffsets the friction loss in the succeeding duct section.

The initial staring velocity in the supply headerdepends on the number of hours of operation. To achievean economic balance between first cost and operatingcost, lower air velocities in the header are recommendedfor 24-hour operation where space permits. When a 90°conical tee is used instead of a 90° tee for the header tobranch take-off, a higher initial staring velocity in thebranch is recommended. The following table suggestsinitial velocities for header and branch duct sizing:

RECOMMENDED INITIAL VELOCITIESUSED WITH CHARTS 12 AND 13 (fpm)

HEADER 12 hr. operation 24 hr. operation

3000 – 40002000 – 3500

BRANCH * 90° conical tee 90° tee

4000 – 50003500 – 4000

Take-Offs To Terminals 2000 maximum* Branches are defined as a branch header or riserhaving 4 to 5 or more take-offs to terminals

Static regain charts are presented for the design ofhigh velocity system. Chart 12 is used for designingbranches and Chart 13 is used for header design. Thebasic difference in the two charts is the air quantity for theduct sections.

Chat 12 is used for sizing risers and branch headershandling 6000 cfm or less. The chart is based on 12 ftincrements between take-offs to the air terminals in thebranches or take-offs to the risers in branch headers. Ascale is provided to correct for spacings more or lessthan 12 ft.

Chat 13 is used to size headers, and has an airquantity range of 1000 to 40,000 cfm. The chart is basedon 20 ft increments between branches. A correction scaleat the top of the chart is used when take-off to branch ismore or less than 20 ft.

Example 6 and 7 are presented to illustrate the useof these two charts. Example 6 is a branch sizingproblem for the duct layout in Fig. 53, and Example 7 is aheader layout (Fig. 55).

Fig. 51 – Spacing of Fitting When Using 90º Conical Tee

Fig. 50 – Spacing of Fitting in Duct Run

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